Important Concepts

Browse key concepts across boards and subjects. Click any concept to see explanation and related questions.

• The quadratic equation $x^{2}+x+1=0$ has $\qquad$ roots.
• If the $\operatorname{HCF}(2520,6600)=40$ and $\operatorname{LCM}(2520,6600)= 252 \times k$, then th
• In the given figure $\triangle \mathrm{ABC}$ is shown. DE is parallel to BC . If $A D=5 \mathrm{~cm}
• If $\sin \theta=\cos \theta,\left(0^{\circ}<\theta<90^{\circ}\right)$, then value of ( $\sec \theta$
• Two dice are rolled together. The probability of getting the sum of the two numbers to be more than
• If $\alpha$ and $\beta$ are zeroes of the polynomial $5 x^{2}+3 x-7$, the value of $\frac{1}{\alpha}
• The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. $\frac{\mathrm
• AB and CD are two chords of a circle intersecting at P. Choose the correct statement from the follow
• If value of each observation in a data is increased by 2 , then median of the new data
• A box contains cards numbered 6 to 55. A card is drawn at random from the box. The probability that
• In the given figure, tangents PA and PB to the circle centred at O , from point P are perpendicular
• $X O Y Z$ is a rectangle with vertices $X(-3,0), O(0,0)$, $\mathrm{Y}(0,4)$ and $\mathrm{Z}(x, y)$.
• Which term of the A.P. $-29,-26,-23, \ldots, 61$ is 16 ?
• In the given figure, AT is tangent to a circle centred at O . If $\angle \mathrm{CAT}=40^{\circ}$, t
• After an examination, a teacher wants to know the marks obtained by maximum number of the students i
• Assertion (A): If $\sin A=\frac{1}{3}\left(0^{\circ}<A<90^{\circ}\right)$, then the value of $\cos \
• Assertion (A): Two cubes each of edge length 10 cm are joined together. The total surface area of ne
• Can the number $(15)^{n}, n$ being a natural number, end with the digit 0 ? Give reasons.
• Find the type of triangle $A B C$ formed whose vertices are $\mathrm{A}(1,0), \mathrm{B}(-5,0)$ and
• $$ 0 \leq \mathrm{A}, \mathrm{~B},(\mathrm{~A}+\mathrm{B}) \leq 90^{\circ} . $$
• In the given figure, AB and CD are tangents to a circle centred at O . Is $\angle B A C=\angle D C A
• Prove that $\sqrt{5}$ is an irrational number.
• Show that $\angle A O B+\angle C O D=180^{\circ}$
• Prove that $\frac{1+\sec \theta-\tan \theta}{1+\sec \theta+\tan \theta}=\frac{1-\sin \theta}{\cos \t
• In a test, the marks obtained by 100 students (out of 50) are given below: | Marks obtained: | $0-1
• In a 2 -digit number, the digit at the unit's place is 5 less than the digit at the ten's place. The
• $$ 3 x+y+4=0 \text { and } 3 x-y+2=0 $$
• From the top of a 45 m high light house, the angles of depression of two ships, on the opposite side
• The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m . Find the area of the secto
• A ball is thrown in the air so that $t$ seconds after it is thrown, its height $h$ metre above its s
• The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment ac
• In a survey on holidays, 120 people were asked to state which type of transport they used on their l
• In the given figure, PT is tangent to a circle with centre O . Chord PQ subtends an angle of $65^{\c
• If $\alpha$ and $\beta$ are zeroes of the polynomial $2 x^{2}-9 x+5$, then value of $\alpha^{2}+\bet
• Value of $k$ for which $x=2$ is a solution of the equation $5 x^{2}-4 x+(2+k)=0$, is
• The sum of first 200 natural numbers is This section consists of 5 questions of 2 marks each.
• The main components of bronze are:
• When 2 mL of sodium hydroxide solution is added to few pieces of granulated zinc in a test tube and
• Select from the following a decomposition reaction in which source of energy for decomposition is li
• A metal and a non-metal that exists in liquid state at the room temperature are respectively: 1
• Carbon compounds: (i) are good conductors of electricity. (ii) are bad conductors of electricity. (i
• Consider the following compounds: $\mathrm{FeSO}_{4} ; \mathrm{CuSO}_{4} ; \mathrm{CaSO}_{4} ; \math
• Oxides of aluminium and zinc are: 1
• $\mathrm{MnO}_{2}+4 \mathrm{HCl} \rightarrow \mathrm{MnCl}_{2}+2 \mathrm{H}_{2} \mathrm{O}+\mathrm{C
• Consider the following statements: (i) The sex of a child is determined by what it inherits from the
• Chromosomes: (i) carry hereditary information from parents to the next generation. (ii) are thread l
• In a nerve cell, the site where the electrical impulse is converted into a chemical signal is known
• A stomata closes when: (i) it needs carbon dioxide for photosynthesis. (ii) it does not need carbon
• At what distance from a convex lens should an object be placed to get an image of the same size as t
• The lens system of the human eye forms an image on a light sensitive screen, which is called as:
• The pattern of the magnetic field produced inside a current carrying solenoid is: 1
• Identify the food chain in which the organisms of the second trophic level are missing: 1
• In which of the following organisms, multiple fission is a means of asexual reproduction? 1 For Q.
• Assertion (A): Hydrogen gas is not evolved when zinc reacts with nitric acid. Reason (R): Nitric ac
• Name the second last element of the period 3.
• Assertion (A): Accumulation of harmful chemicals is maximum in the organisms at the highest trophic
• Assertion (A): The rate of breathing in aquatic organisms is much faster than in terrestrial organis
• Assertion (A): The rainbow is a natural spectrum of sunlight in the sky. Reason (R): Rainbow is form
• Name the type of chemical reaction in which calcium oxide reacts with water. Justify your answer by
• State one role of each of the following in human digestive system: (i) Hydrochloric acid (ii) Villi
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• An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm . Find the pos
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• (i) Two magnetic field lines do not intersect each other. Why? 2 (ii) How is a uniform magnetic fie
• Write one chemical equation each for the chemical reaction in which the following have taken place:
• (i) The pH of a sample of tomato juice is 4.6. How is this juice likely to be in taste? Give reason
• (i) Why is respiratory pigment needed in multicellular organisms with large body size? 1 (ii) Give r
• Define reflex action. With the help of a flow chart, show the path of a reflex action such as sneezi
• Study the diagram given below and answer the questions that follow: 3 (i) Name the defect of visio
• Name and state the rule to determine the direction of a: 3 (i) magnetic field produced around a curr
• In the given food chain, what will be the impact of removing all the organisms of second trophic lev
• 5 (ii) Why is the melting and boiling points of $\mathrm{C}_{4} \mathrm{H}_{8}$ higher than that of
• (ii) What will happen if in a human female (a) fertilisation takes place, (b) an egg is not fertilis
• How many elements are in the second period?
• (ii) An electric oven is designed to work on the mains voltage of 220 V . This oven consumes 11 unit
• The metals produced by various reduction processes are not very pure. They contain impurities, which
• Mendel worked out the rules of heredity by working on garden pea using a number of visible contrasti
• Study the data given below showing the focal length of three concave mirrors $\mathrm{A}, \mathrm{B}
• The name and formula of third member of homologous series of alkyne is: 1
• A ray of light falls making an angle of incidence 0 on the surface of a glass slab. Draw a labelled
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• Mention the pathway of urine in our body starting from the organ of its formation to its excretion.
• Translate the following statements into chemical equations and then balance them: 2 (i) Solution of
• In the context of the statement "chlorophyll is necessary for photosynthesis" answer the following q
• A narrow beam, PQ of white light is passing through a glass prism ABC as shown in the diagram. Draw
• (i) Name two safety measures commonly used in electric circuits and appliances. 3 (ii) The power ra
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• A polar covalent compound is:
• Which one of the following organ is NOT a part of human female reproductive system? 1
• In bifocal lenses used for the correction of presbyopia:
• (ii) How is human brain protected from mechanical injuries and shocks? 2
• (i) Give reason why herbivorous animals have longer, small intestine than carnivorous animals? 2 (i
• Translate the following statement into a balanced chemical equation. When barium chloride reacts wit
• Draw the pattern of the magnetic field lines due to a straight current carrying conductor indicating
• (i) Which organisms have a three-chambered heart? Why do they have three-chambered hearts? 3 (ii) Li
• A compound which is prepared from gypsum has the property of hardening when water is mixed in right